I'm reviewing my first semester of AP Calculus. While doing some review questions, I came across these two problems.
I started manipulating the derivative notation in order to get the solution, but how do I continue this problem?
I'm reviewing my first semester of AP Calculus. While doing some review questions, I came across these two problems.
I started manipulating the derivative notation in order to get the solution, but how do I continue this problem?
(1) $\displaystyle y = \sqrt{x^2+1}$
$\displaystyle y^2 = x^2 + 1$
$\displaystyle \frac{d}{dx^2}(y^2 = x^2 + 1)$
$\displaystyle \frac{dy^2}{dx^2}= 1$
(2) let $\displaystyle u = \frac{1}{1-x}$
$\displaystyle \frac{du}{dx} = \frac{1}{(1-x)^2}$
$\displaystyle y = x^2+x$
$\displaystyle \frac{dy}{dx} = 2x+1$
$\displaystyle \frac{dy}{du} = \frac{\frac{dy}{dx}}{\frac{du}{dx}} = (2x+1) \cdot (1-x)^2$